Lasso Is Just a Laplace Prior

2026-06-22 · Source: DataMListic · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Intermediate, quick

Summary

Lasso regression exhibits an "all or nothing" behavior, aggressively snapping many feature coefficients to exactly zero, unlike Ridge regression which merely shrinks them. This distinction is clarified by reframing the penalty term in regularized regression as a Bayesian prior. Ridge's squared penalty term corresponds to a Gaussian prior, a smooth distribution that prefers small weights but never truly zero. In contrast, Lasso's absolute value penalty term encodes a Laplace prior, characterized by a razor-sharp peak precisely at zero. This high probability density at zero means that for weak weights, zero is the single most likely value. Therefore, Lasso's feature deletion is not an optimization trick but a direct outcome of its inherent belief that most weights are zero.

Key takeaway

For Machine Learning Engineers selecting regularization techniques, understand that Lasso's aggressive coefficient-to-zero behavior is not merely an optimization trick. Your choice of Lasso implicitly assumes a Laplace prior, meaning you believe most features are irrelevant and their weights should be zero. Conversely, Ridge assumes a Gaussian prior, preferring small but non-zero weights. Align your regularization choice with your prior beliefs about feature importance to build more interpretable and robust models.

Key insights

Lasso's feature selection stems from its implicit Laplace prior, which strongly favors zero coefficients for weak weights.

Principles

• Regularized regression penalties are Bayesian priors.
• Ridge uses a Gaussian prior, preferring small weights.
• Lasso uses a Laplace prior, preferring zero weights.

Topics

• Lasso Regression
• Ridge Regression
• Bayesian Statistics
• Regularization
• Laplace Prior
• Gaussian Prior

Best for: AI Scientist, Machine Learning Engineer, Data Scientist

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• Canonical Regularisation of Wide Feature-Learning Neural Networks — Traditional ridge regularization biases feature-learning networks due to curved parameter-space geometry, necessitating a geodesic-based approach.
• Lasso Regression: Why the Solution Lives on a Diamond — Lasso Regression uses vector projections and coefficient constraints to prevent overfitting by shrinking feature coefficients.

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Editorial summary, takeaway, and curation by AIssential. Original article published by DataMListic.